What is the difference between "shell" and a "membrane" in terms of loading as applied to structures?

In brief I can answer you like this:

Membranes have in-plane stiffness : like a shear wall

Plates are elements with out-plane stiffness like a concrete slab (though we model slabs as membranes in Structural Analysis programs like Etabs to solve the problem easire)

Shells are a combination of both like a retaining wall

membranes only transfer in-plane forces and perpendicular moments as results of in-plane tensions and compressions. it has SDOF in rotation and2 DOF in displacement.

Plates can only endure Moments and lateral out-plane shears. it has SDOF in displacement and2 DOF in rotation.

Shell = Plate + Membrane

it has6 Degree Of Freedom.

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